5. Ohm's Law and Resistance

Ohm's Law

Ohm's law, formulated by the German physicist Georg Simon Ohm in 1827, is the single most important quantitative relationship in basic electricity and is a near-certainty to appear in every SSC/RRB paper in some form. It states that, at a constant temperature, the current flowing through a conductor is directly proportional to the potential difference applied across its two ends, provided the physical conditions (especially temperature) of the conductor remain unchanged. Mathematically, this is written as V = IR, where V is the potential difference in volts, I is the current in amperes, and R is a constant of proportionality called the resistance of the conductor, measured in ohms. Rearranged, R = V/I, which gives the operational definition of resistance.

Materials or components that obey Ohm's law over a wide range of conditions (that is, whose V–I graph is a straight line through the origin) are called ohmic conductors — most pure metals at constant temperature behave this way. Components such as diodes, transistors, and electrolytes generally do not obey a simple linear V–I relationship and are called non-ohmic conductors.

Resistance and the Factors Affecting It

Resistance is the opposition that a conductor offers to the flow of electric current through it; it arises because moving electrons collide with the fixed atoms/ions of the conducting material, converting some electrical energy into heat. The resistance of a given conductor depends on four factors, captured in the formula:

R = ρ · L / A

• Length (L): Resistance is directly proportional to the length of the conductor. A longer wire offers more resistance because charge carriers must travel farther and undergo more collisions.
• Area of cross-section (A): Resistance is inversely proportional to the cross-sectional area of the conductor. A thicker wire offers less resistance because it provides more parallel paths for electrons to move through.
• Nature of material (resistivity, ρ): Different materials offer different intrinsic resistance per unit length per unit area, a property called resistivity (or specific resistance), denoted ρ. Resistivity depends only on the material (and temperature), not on the conductor's dimensions. Silver has the lowest resistivity among common metals, followed by copper; this is precisely why copper is the standard choice for household and industrial wiring — an excellent balance of low resistivity and low cost. Alloys such as nichrome (used in heating elements) have deliberately high resistivity and are also highly resistant to oxidation at high temperatures.
• Temperature: For most metallic conductors, resistance increases as temperature increases, because the increased thermal vibration of atoms causes more frequent collisions with the moving electrons. This is why the resistance of a filament bulb is much higher when it is glowing (hot) than when it is cold. Conversely, for semiconductors and insulators, resistance generally decreases as temperature increases.

Unit of Resistance: The SI unit of resistance is the ohm, denoted by the Greek letter Ω (omega), named after Georg Simon Ohm. One ohm is defined as the resistance of a conductor such that a potential difference of one volt across it produces a current of one ampere through it (1 Ω = 1 V/A). The reciprocal of resistance is called conductance, measured in siemens (S).